I saw emails from English people with Many Thanks as a signing off phrase. Is that proper usage? Or is it a phrase created by continental English speakers due to the influence of their native language? (Vielen Dank in German and muchas gracias in Spanish translate to "many thanks".)

I have seen several other cases where one constructs imprecise sentences due to the influence of native language. This is evident especially in India.

As Martha says, many thanks is perfectly idiomatic. However, it is indeed an oddly isolated idiom: most other constructions which try to treat thanks as a plural noun are ungrammatical (eg *lots of thanks), and there’s certainly no such thing as *a thank.

In the sense of “feelings of gratitude” it can be used either as a mass noun (thanks is due to God for this harvest…), or a plural (thanks are due to God…). In the sense of “expressions of gratitude”, it can be used as either of these, or also as a singular: a special thanks is due to the chairman…

[Sources for this: roughly counting hits for phrasings like thanks is, thanks are in Google and COHA.]

How did it get this way? The entries for thanks in the OED tell a tangled tale, but as far as I can make out, thank was originally an acceptable singular noun (their last citation is 1642, Is this the thanke which you returne to God?), but the plural form thanks gradually predominated, and apparently lost its plural-ness to some extent.

This bit is confusing: the OED describes thanks here as “†Formerly sometimes construed as singular”, and their citations where it’s unambiguously singular stop after Shakespeare (1594, Thanks to men Of Noble minds, is honourable meede.), but all the later citations they give are completely ambiguous about its number (1805, I return it to you with my sincere thanks.), like most modern usage. There are no citations where it’s unambiguously treated as plural.

Their earliest citation for the phrase Many thanks is 1803, Many thanks for your letter. So this seems to arise some while after thanks was generally construed as plural! I’d love to know more of the background here…

It all depends on your perspective. You can break it down far enough so that there's no way it's proper: What is a "thank?" Can such a thing be pluralized? Taken on its own, "many thanks" is a sentence fragment, and thus not truly proper.

In common use, though, I'd say it's a standard closing for a communication, like "With kind regards, Joe Blow" and is entirely acceptable (though I admit that I don't care for using things like "many thanks" without also including the sender's name as a signature). It's vernacular, which is to say it's how the language is used, regardless of how proper it is grammatically speaking.

@NeilFein it can be a bit rude. IMHO it works better when you already know the person is going to do what you've asked them to do, e.g. when you are following up on a request that you've already made verbally. If you were cold-calling via e-mail, it could be considered a tad presumptuous. In any case, there are far worse things you could do in e-mail: I give you the exclamation mark (!) as an example. Consider "many thanks" vs. "many thanks!" and see if you can tell whether it is an exclamation or just sarcasm...
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ukayerMar 25 '12 at 6:45